CN108761387B - Double-station time difference and frequency difference combined positioning method for fixed radiation source - Google Patents

Double-station time difference and frequency difference combined positioning method for fixed radiation source Download PDF

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CN108761387B
CN108761387B CN201810559098.2A CN201810559098A CN108761387B CN 108761387 B CN108761387 B CN 108761387B CN 201810559098 A CN201810559098 A CN 201810559098A CN 108761387 B CN108761387 B CN 108761387B
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radiation source
target
equation
radial distance
difference
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CN108761387A (en
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杨洁
刘聪锋
苏娟
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Xian University of Posts and Telecommunications
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/16—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using electromagnetic waves other than radio waves

Abstract

A double-station time difference and frequency difference combined positioning method for a fixed radiation source comprises the following steps: 2, receiving electromagnetic wave signals emitted by a target radiation source by using observation stations to obtain time difference and frequency difference measurement information; determining a time difference and frequency difference positioning equation:
Figure DDA0001682732190000011
establishing a target position equation:
Figure DDA0001682732190000012
establishing a radial distance equation: k is a radical of6r1 6+k5r1 5+k4r1 4+k3r1 3+k2r1 2+k1r1+k00; solving a radial distance equation to obtain a radial distance between the 1 st observation station and a target radiation source; according to the obtained radial distance r between the 1 st observation station and the target radiation source1And calculating target position parameters by using a target position equation to complete the positioning of the target radiation source. The method adopts a time difference and frequency difference combined positioning method, converts the nonlinear equation set into the linear equation set by using the radial distance, has simple calculation and high positioning speed, and can realize high-precision estimation of the position of the fixed radiation source on the given plane.

Description

Double-station time difference and frequency difference combined positioning method for fixed radiation source
Technical Field
The invention belongs to the technical field of passive positioning, and particularly relates to a double-station time difference and frequency difference combined positioning method for a fixed target radiation source in electronic reconnaissance application.
Background
In the electronic countermeasure field, the higher the reconnaissance precision of radiation source position information is, the more help carries out effectual information acquisition, electronic interference and accurate striking to the radiation source, provides the sound guarantee for finally destroying the target. Passive localization techniques for radiation sources therefore hold a very important position in the field of electronic countermeasures. Among the current passive positioning technologies, the passive time difference positioning system is the most concerned research technology due to the advantages of high positioning accuracy, strong networking working capability, strong anti-strike capability and the like. However, the time difference method positioning often causes a fuzzy problem due to the occurrence of a plurality of values in the solution of the appropriate equation, so that the positioning method has limitations in positioning high repetition frequency and high maneuvering targets.
When relative motion exists between the observation stations and the radiation source, the target can be positioned by using the frequency difference of signals reaching each observation station so as to make up for the defect of time difference positioning ambiguity. The target position is positioned by combining the frequency difference and the time difference, so that the positioning precision can be improved. In the combined time difference and frequency difference combined positioning technology, a plurality of observation stations simultaneously receive and process radiation source signals to determine a plurality of positioning curved surfaces (such as planes, hyperboloids, circles and the like), and the intersection positions of the plurality of positioning curved surfaces are estimated positions of targets. However, the existing time difference and frequency difference joint positioning method is applied to a plurality of observation stations, and may obtain a plurality of intersection points, i.e. a plurality of target position estimated values, thereby also bringing a fuzzy problem. How to overcome the defect that the existing time difference and frequency difference combined composite positioning technology has ambiguity, further improve the target position estimation precision and enlarge the reconnaissance range, and has important significance for the development of electronic reconnaissance technology.
Disclosure of Invention
The invention aims to provide a time difference and frequency difference combined positioning method for a fixed target radiation source, which can improve the estimation precision.
In order to achieve the purpose, the invention adopts the following technical scheme:
a double-station time difference and frequency difference combined positioning method for a fixed radiation source comprises the following steps:
acquiring time difference and frequency difference measurement information, wherein 2 observation stations receive electromagnetic wave signals emitted by a target radiation source to acquire time difference and frequency difference measurement information;
determining a time difference and frequency difference positioning equation, wherein the time difference and frequency difference positioning equation is as follows:
Figure BDA0001682732170000021
wherein r is21The radial distance difference between the target radiation source and the 2 nd observation station and between the target radiation source and the 1 st observation station,
Figure BDA0001682732170000022
is r21Rate of change of siIs the position coordinate vector of the ith observation station,
Figure BDA0001682732170000023
for the velocity vector of the ith observation station, i ═ 1,2, (·)TDenotes a transpose operation, u being the position coordinate vector of the target, r1The radial distance between the 1 st observation station and the target radiation source,
Figure BDA0001682732170000024
is r1The rate of change of (c);
establishing a target position equation, wherein the target position equation is as follows:
Figure BDA0001682732170000025
in the formula a1、a2、b1、b2、c1、c2、d1、d1、e1、e2Are all and r1An irrelevant coefficient;
establishing a radial distance equation, wherein the radial distance equation is as follows:
Figure BDA0001682732170000026
k in the formula0、k1、k2、k3、k4、k5、k6Are all and r1An irrelevant coefficient;
calculating the radial distance, solving a radial distance equation to obtain the radial distance r between the 1 st observation station and the target radiation source1；
Calculating the position of a target radiation source according to the obtained radial distance between the 1 st observation station and the target radiation sourcer1And calculating target position parameters by using a target position equation to complete the positioning of the target radiation source.
More specifically, the rate of change of the radial distance
Figure BDA0001682732170000027
More specifically, the coefficient a in the target position equation1、a2、b1、b2、c1、c2、d1、d1、e1、e2Determined by the following formula:
Figure BDA0001682732170000031
Figure BDA0001682732170000032
Figure BDA0001682732170000033
Figure BDA0001682732170000034
Figure BDA0001682732170000035
x in the formulai、yi、ziRespectively the position coordinate component of the ith observation station in the direction X, Y, Z,
Figure BDA00016827321700000310
the velocity components of the ith observation station in the direction X, Y, Z, i ═ 1,2, zTIs the height of the plane of the target radiation source.
More specifically, the coefficient k in the radial distance equation0、k1、k2、k3、k4、k5、k6Determined by the following formula:
Figure BDA0001682732170000036
Figure BDA0001682732170000037
Figure BDA0001682732170000038
Figure BDA0001682732170000039
Figure BDA0001682732170000041
Figure BDA0001682732170000042
further, the 2 observation stations are arranged in parallel and are not on the same horizontal plane.
Further, 2 observation stations are in the same vertical plane.
According to the technical scheme, when the passive positioning is carried out on the fixed radiation source, the time difference and frequency difference combined positioning method is adopted, the radial distance is utilized to convert the nonlinear time difference and frequency difference positioning equation into a linear equation set, a target position equation related to the radial distance is obtained, then the target position equation is substituted into the radial distance equation, the radial distance of the target relative to the 1 st observation station is solved, the radial distance obtained through calculation is utilized, and the accurate estimation of the position of the target radiation source is realized according to the target position equation. The method can calculate the target position by only directly solving the root of the sextic polynomial in the radial distance equation, has simple calculation and high positioning speed, can realize high-precision estimation of the position of the fixed radiation source on a given plane, and has important effects on obtaining effective battlefield information, implementing electronic interference and efficiently striking enemy targets. The method is suitable for three-dimensional positioning, does not need the earth constraint condition, can quickly obtain high-precision estimation of the target position, and can be applied to the passive positioning scene of a moving double-station to a fixed radiation source on a given plane in electronic reconnaissance.
Drawings
Fig. 1 is a schematic diagram of the two-station positioning of the present invention.
FIG. 2 is a flow chart of the method of the present invention.
The following describes embodiments of the present invention in further detail with reference to the accompanying drawings.
Detailed Description
The time difference and frequency difference combined positioning method is to use the measurement information of time difference and frequency difference to carry out passive positioning, and under the condition that the time difference and frequency difference measurement information of signals, the position parameters of each observation station and the height of a target are obtained, the positioning of the target is a problem of solving a nonlinear equation set. The basic idea of the method of the invention is as follows: converting the nonlinear equation set into a linear equation set through radial distance, expressing a solving equation of the target position by using the radial distance, solving the radial distance of the target relative to 1 observation station by using the radial distance equation, and realizing accurate estimation of the target position by using the obtained target position equation.
The technical solutions of the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1 and 2, the method of the present invention comprises the following steps:
s100, acquiring time difference and frequency difference measurement information; in a three-dimensional space, two moving observation stations (a 1 st observation station and a 2 nd observation station) receive electromagnetic wave signals emitted by a fixed target radiation source in a given plane to obtain time difference and frequency difference measurement information, wherein three coordinate axes of a rectangular coordinate system in the three-dimensional space are X, Y, Z (figure 1);
s200, determining a time difference and frequency difference positioning equation; determining a time difference and frequency difference positioning equation according to the time difference and frequency difference observation information, wherein the time difference measurement information comprises the difference value (r) between the radial distance between the target radiation source and the 2 nd observation station and the radial distance between the target radiation source and the 1 st observation station21) The frequency difference measurement information includes a rate of change of the radial distance difference
Figure BDA0001682732170000051
The equation of time difference and frequency difference location is:
Figure BDA0001682732170000052
wherein r is21The radial distance difference between the target radiation source and the 2 nd observation station and between the target radiation source and the 1 st observation station,
Figure BDA0001682732170000053
is r21Is rate of change, i.e.
Figure BDA0001682732170000054
siIs the position coordinate vector of the ith observation station,
Figure BDA0001682732170000055
for the velocity vector of the ith observation station, i ═ 1,2, (·)TDenotes a transpose operation, u being the position coordinate vector of the target, r1The radial distance between the 1 st observation station and the target radiation source,
Figure BDA0001682732170000056
is r1The rate of change of (a) is,
Figure BDA0001682732170000057
position coordinate vector s of ith observation stationi＝(xi,yi,zi)T，xi、yi、ziThe position coordinate component of the ith observation station in the direction of X, Y, Z and the velocity vector of the ith observation station
Figure BDA0001682732170000058
The velocity components of the ith observation station in the direction of X, Y, Z are respectively, i is 1 and 2, and the above parameters can be directly measured; the position coordinate vector u of the target is (x, y, z)T)TX is the component of the target position in the X direction, Y is the component of the target position in the Y direction, X and Y are the parameters to be estimated, zTThe height of the plane where the target radiation source is located is given;
s300, establishing a target position equation; simultaneous time and frequency difference positioning equation using radial distance r between target radiation source and observation station No. 11Representing target position parameters x, y, the target position equation is:
Figure BDA0001682732170000061
in the formula a1、a2、b1、b2、c1、c2、d1、d1、e1、e2Are all and r1The independent coefficients can be determined according to the following formula:
Figure BDA0001682732170000062
Figure BDA0001682732170000063
Figure BDA0001682732170000064
Figure BDA0001682732170000065
Figure BDA0001682732170000066
s400, establishing a radial distance equation; the radial distance equation of the present invention is with respect to r1Is obtained from the position coordinate vector of the 1 st observation station and the position coordinate vector of the target
Figure BDA0001682732170000067
Is unfolded
Figure BDA0001682732170000068
The radial distance equation is obtained as:
Figure BDA0001682732170000069
k in the formula0、k1、k2、k3、k4、k5、k6Are all and r1The independent coefficients can be determined according to the following formula:
Figure BDA00016827321700000610
Figure BDA00016827321700000611
Figure BDA00016827321700000612
Figure BDA0001682732170000071
Figure BDA0001682732170000072
Figure BDA0001682732170000073
Figure BDA0001682732170000074
s500, calculating the radial distance r between the 1 st observation station and the target radiation source1(ii) a Solving the one-dimensional multiple equation (radial distance equation) obtained in step S400 by using a mathematical method, such as a polynomial root-finding method, a Newton method and the like, wherein the root of the obtained one-dimensional multiple equation is the radial distance r between the 1 st observation station and the target radiation source1；
S600, calculating the position of a target radiation source; according to the radial distance r between the 1 st observation station and the target radiation source obtained in the step S4001And substituting the target position parameters into the target position equation in the step S300 to calculate target position parameters x and y, and finishing accurate positioning of the target radiation source.
In step S500, the radial distance r between the 1 st observation station and the target radiation source is calculated1When the radial distance equation is a unitary multiple equation, a plurality of roots can be obtained when the unitary multiple equation is solved, wherein one positive real root is r1The true value of (d). To avoid the problem of positioning ambiguity, i.e. to avoid r1In step S600, the fuzzy problem may be determined according to the prior information, and the false values in the prior information are removed, for example, the false positioning result is removed by combining with target intelligence information provided by other reconnaissance devices or according to the approximate position information of the target, and the method adopted in this embodiment is as follows: through observation and accumulation at multiple moments, clustering analysis is carried out on positioning results of the multiple observation moments (the existing method is adopted for the clustering analysis), and fuzzy estimation values are eliminated because estimation values of target positions are concentrated near real values.
R solved by polynomial root method1To locate a fixed radiation source in a given plane, the root mean square error of the target position estimate decreases with increasing continuous observation time, and measurement errors decrease with increasing measurement timeThe difference is increased, namely the longer the continuous observation time is, the smaller the measurement error is, the better the positioning effect of the method on the target is, and the higher the positioning precision of the target radiation source in the fields of electronic reconnaissance, weapon guidance and the like is. Further, under the conditions of the same continuous observation time and the same measurement error, when the two observation stations are configured in parallel to realize the positioning of the target radiation source, the situation that the two observation stations are configured in parallel on the same horizontal plane should be avoided, because the positioning result error under the situation is very large; meanwhile, in order to improve the accuracy of real-time positioning, the situation that the two observation stations do not move in the same horizontal plane but are still arranged in parallel should be adopted as much as possible, and when the two observation stations are not in the same horizontal plane but arranged in parallel in the same vertical plane, the position estimation error is minimum, and the positioning effect is best.
According to the time difference and frequency difference positioning equation, the method is suitable for passive positioning under the condition that the number of observation stations is suitable (the number of the time difference and frequency difference equation is the same as the number of unknown parameters of the target position) and under the condition of low measurement error; the change of the central frequency of the signal radiated by the target radiation source does not influence the positioning precision of the target by the method, namely the change of the central frequency of the signal is irrelevant to the target position error finally solved by the algorithm; in the process of realizing passive positioning by using the method, the ambiguity problem of the solution can be solved by observing for many times and carrying out cluster analysis on the observation result.
Although the present invention has been described with reference to a preferred embodiment, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (4)

1. A double-station time difference and frequency difference combined positioning method for a fixed radiation source is characterized by comprising the following steps:
acquiring time difference and frequency difference measurement information, wherein 2 observation stations receive electromagnetic wave signals emitted by a target radiation source to acquire time difference and frequency difference measurement information;
determining a time difference and frequency difference positioning equation, wherein the time difference and frequency difference positioning equation is as follows:
Figure RE-FDA0003320418500000011
wherein r is21The radial distance difference between the target radiation source and the 2 nd observation station and between the target radiation source and the 1 st observation station,
Figure RE-FDA0003320418500000012
is r21Rate of change of siIs the position coordinate vector of the ith observation station,
Figure RE-FDA0003320418500000013
for the velocity vector of the ith observation station, i ═ 1,2, (·)TDenotes a transpose operation, u being the position coordinate vector of the target, r1The radial distance between the 1 st observation station and the target radiation source,
Figure RE-FDA0003320418500000014
is r1The rate of change of (c);
establishing a target position equation, wherein the target position equation is as follows:
Figure RE-FDA0003320418500000015
in the formula a1、a2、b1、b2、c1、c2、d1、d2、e1、e2Are all and r1Independent coefficient, coefficient a1、a2、b1、b2、c1、c2、d1、d2、e1、e2Determined by the following formula:
Figure RE-FDA0003320418500000016
Figure RE-FDA0003320418500000017
Figure RE-FDA0003320418500000018
x in the formulai、yi、ziRespectively the position coordinate component of the ith observation station in the direction X, Y, Z,
Figure RE-FDA0003320418500000019
the velocity components of the ith observation station in the direction X, Y, Z, i ═ 1,2, zTThe height of the plane of the target radiation source;
establishing a radial distance equation, wherein the radial distance equation is as follows:
Figure RE-FDA0003320418500000021
k in the formula0、k1、k2、k3、k4、k5、k6Are all and r1Independent coefficient, coefficient k0、k1、k2、k3、k4、k5、k6Determined by the following formula:
Figure RE-FDA0003320418500000022
Figure RE-FDA0003320418500000023
Figure RE-FDA0003320418500000024
Figure RE-FDA0003320418500000025
Figure RE-FDA0003320418500000026
Figure RE-FDA0003320418500000027
Figure RE-FDA0003320418500000028
calculating the radial distance, solving a radial distance equation to obtain the radial distance r between the 1 st observation station and the target radiation source1；
Calculating the position of a target radiation source according to the obtained radial distance r between the 1 st observation station and the target radiation source1And calculating target position parameters by using a target position equation to complete the positioning of the target radiation source.
2. The method for the dual-station time-difference frequency-difference joint positioning of the fixed radiation source according to claim 1, wherein: rate of change of radial distance
Figure RE-FDA0003320418500000031
3. The method for the dual-station time-difference frequency-difference joint positioning of the fixed radiation source according to claim 1, wherein: the 2 observation stations are arranged in parallel and are not on the same horizontal plane.
4. A method for the dual-station moveout-frequency-difference joint positioning of a stationary radiation source as claimed in claim 3, characterized in that: the 2 observation stations are in the same vertical plane.
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